Singular perturbation approach to an elastic dry friction problem with non-monotone coefficient

Yves Renard (1)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul

In this paper, we study a one-dimensional dynamical model of dry friction with slip velocity dependent coefficient. In many cases, this model has more than one solution. We introduce a perturbed friction condition which allows to recover the uniqueness of the solution. We show that perturbated problem solutions pointwise converge to a particular solution of the initial problem when the perturbation parameter tends to zero. The singular perturbation approach provides the analysis of a criterion used to select a solution of the problem, and suggests a method to study more elaborated dry friction problems.

Mots clés: Boundary layers; Coefficient of friction; Dry friction; Sliding; Differential equations; Cauchy problem

Domaines: Analyse numérique [math.NA]

Yves Renard. Singular perturbation approach to an elastic dry friction problem with non-monotone coefficient. Quarterly of Applied Mathematics, 2000, LVIII (2), pp.259-272. ⟨10.1090/qam/1753401⟩. ⟨hal-00690555⟩